Unprecedented changes in the terms of trade

Transcription

1 Unprecedented changes in the terms of trade Mariano Kulish and Daniel M. Rees September 9, 214 Preliminary Draft Abstract The development of Asia exposed many commodity-exporting economies to unprecedented changes of their terms of trade. We set up a small open economy model to estimate the magnitude and timing of breaks in the long-run level and variance of the terms of trade. The model s balanced growth path gives rise to wedges between tradable, headline, and non-tradable rates of inflation and between the growth rates of investment and aggregate output as a result of multiple productivity trends that trigger off drifts in relative prices as in the data. Using Australian unfiltered aggregate data, we find evidence of an increase in the long-run level and volatility of the terms of trade. Single-equation structural break tests point to a larger increase in the long-run level of the terms of trade. But inferences in general equilibrium rely on many observables that also respond to shifts in the long-run level of the terms of trade. For comments and discussions we thank James Morley, Tim Robinson and Adrian Pagan. The usual disclaimer applies. School of Economics, UNSW, m.kulish@unsw.edu.au Economic Research, Reserve Bank of Australia reesd@rba.gov.au Please do not circulate without the authors consent. 1

2 1 Introduction Over the past two decades, the increasing development of Asia has exposed many economies to a surge in global commodity prices. There have been commodity price booms before, but this one, fueled by an unprecedented era of high growth in China, has been by far the largest and most persistent. In response, policy makers, market economists and the press in these economies have entertained the idea that commodity prices have reached a new normal, with a permanently higher level and greater volatility. 1 Understanding whether the terms of trade of commodity-exporting economies have reached a new normal and its implications for these economies has become of first order importance. 2 Measuring the macroeconomic impact of unprecedented changes in the terms of trade is a considerable task because the models used to study business cycles in small open economies are typically solved and estimated around a constant unconditional mean, but the idea of a new normal points to a shift of the unconditional mean. Moreover, changes in the terms of trade affect many relative prices that in the data trend at different rates, in particular the price of non-tradable goods and the price of investment goods. When estimating small open economy models, it is common to abstract from many of these trends and to resort to pre filtering the data somehow. While pre filtering aligns the data with the model, it comes at the cost of distorting the facts. As Beneš et al. [29] point out, a limitation of this approach is that it treats trends and cycles separately. In this paper we have gone to some effort to develop a unified model of the trends that we see in the data and to estimate it in the presence of shifts in the long-run level of the terms of trade. We add sector-specific productivity trends to an otherwise standard small open economy model that has nominal price frictions, imperfect exchange rate passthrough, capital accumulation and investment adjustment costs as well as a tradable, a non-tradable and a commodity-exporting sector. On the balanced growth path relative prices trend at different rates but nominal expenditure shares remain constant. In the model as in the data non-tradable goods prices run faster than consumer goods prices which run faster than tradable goods prices which, in turn, run faster than investment goods prices, while real investment and foreign output grow faster than domestic output. One significant contribution of this paper is to set up a small open economy that can account for these observed trends. The long-run level of the terms of trade, among other parameters, determines the balanced growth path, so a permanent change of the long-run level of the terms of trade gives rise to a transition towards a new balanced growth path that temporarily affects relative prices. It is an empirical issue to identify trends that belong to the balanced growth path, cycles around those trends, and fluctuations that originate from a transition towards a new balanced growth path. This is what we do in this paper. One contribution is to show how these forces may be identified in the data. Australia is an example of a commodity-exporting economy exposed to the rise of Asia. 1 See Bernanke [28], Bloxham et al. [212], Stevens [211], Tasker [213] and Yellen [211]. 2 The implications of commodity price booms are likely to differ among economies that produce commodities and those that consume them. Our focus here is on the impact of commodity price booms in commodity-exporting economies. Because for commodity-exporting economies the bulk of recent terms of trade fluctuations come from commodity prices movements, we use these terms interchangeably. 2

3 Over the past two decades, the foreign currency price of Australia s commodity exports increased by more than 2 per cent. 3 As Figure 1 shows, Australia s commodity prices are representative of world commodity prices which suggests that many other commodity exporting economies have experienced similar fluctuations as well. For these reasons, we estimate the model on Australian aggregate data. Figure 1: Commodity Price Indices Index 3 Australia Index World * Deflated by US CPI; average = 1 Sources: IMF; RBA We find that the long-run level of commodity prices increased by 4 per cent in mid 23. An increase of this magnitude is probably less than what would be inferred from visual inspection of Figure 1; it is also less than the 9 per cent increase suggested by single equation structural break tests. Our inferences, however, rely on more observables: an increase of 9 per cent is unlikely, but not because commodity prices would disagree, but because other observables series would disagree. The estimated long-run properties of the economy in our case depend on the cross-equations restrictions that rational expectations imposes on every observable series. This is not to say, however, that the 4 per cent increase we estimate in the longrun level of commodity prices has no significant impact. In fact, some of the economic implications are these: the commodity sector s share of exports increases from 35 to 52 per cent; the non-commodity tradable sector s share of value added decreases from 36 to 32 per cent; inflation falls by 2 percentage points with tradable inflation and nontradable inflation rates strongly offsetting each other; the relative price of non-tradable goods increase by 7 per cent and the real exchange appreciates permanently by 3 per cent. 3 Other structural features of the Australian economy, including its monetary policy regime, have remained stable over the past two decades. 3

4 Our work builds on that of Rabanal [29] and Siena [214], who set up models with different productivity trends in the tradable and non-tradable sectors. We add capital accumulation with a differential trend in the productivity of the investment goods producing sector as well as a commodity-exporting goods producing sector that takes the relative price of its output as given. Our work relates to a large literature on the role of terms of trade shocks in open economies to which we cannot possibly do justice. 4 Mendoza [1995] studies the contribution of terms of trade shocks to the business cycle in a calibrated open economy RBC model and finds that terms of trade shock account for 5 per cent of output fluctuations. Other papers, like Dib [28] and Medina and Soto [27], study the impact of terms of trade shocks in DSGE models with nominal frictions. Our work is different because we distinguish temporary shocks to the terms of trade which has been the focus in the small open literature from permanent shifts of the long-run level of the terms of trade. The rest of the paper is structured as follows. Section 2 discusses the model. Many details can be found in the online appendix. 5 Section 3 discusses our empirical approach which involves calibration and estimation of date breaks and parameters. Section 4 describes the main results. Section 5 analyses the responses of the estimated model to temporary and permanent changes in the terms of trade. Section 6 concludes suggesting avenues for further research. 2 Model We extend the standard small open economy model with nominal rigidities in the following ways. 6 We include capital accumulation, non-tradable and commodity-exporting sectors; and we include trends, following Rabanal [29], in sector-specific productivity technology processes to give rise to inflation differentials in steady state. We add Rotemberg [1982] style price adjustment costs in the home-produced tradeable, non-tradeable and import sectors. Sector-specific capital and investment adjustment costs restrict the economy s ability to adjust the composition of output in response to shocks. To help the model match the empirical volatility of many observables we include intertemporal and labour market preference shocks, investment-specific productivity shocks and risk premium shocks to the uncovered interest parity equation. Since the model is large, we present the basic ingredients in the main text and leave a comprehensive presentation to the appendix. 4 Instead, we point the reader to Ostry and Reinhart [1992], Bidarkota and Crucini [2], Bleaney and Greenaway [21], Broda [24], Blattman et al. [27], Jääskelä and Smith [213], Charnavoki and Dolado [214] and the references therein. 5 ADD LINK. 6 For a version of the small open model with nominal rigidities see, for example, Gali and Monacelli [25]. 4

5 2.1 Households The preferences of a typical household in the small open economy are given by: IE t= β t ζ t U (C t, L t ) where IE denotes the time conditional expectation, β is the discount factor and the preference shock ζ t follows the autoregressive process: ln ζ t = ρ ζ ln ζ t 1 + u ζ,t (1) where ρ ζ < 1 and u ζ,t is an identically and independently distributed (iid) random variable with mean zero and standard deviation σ ζ. The single period utility function U is strictly increasing in aggregate consumption, C t, decreasing in hours worked, L t, and given by: L 1+ν t U(C t, L t ) = ln(c t hc t 1 ) ε L,t 1 + ν where h [, 1] governs the degree of external habit formation and ν controls the responsiveness of aggregate labour supply to changes in real wages. ε L,t is a labour supply shock that follows: ln ε L,t = ρ ε ln ε L,t 1 + u L,t (2) where ρ ε < 1 and u L,t is an iid random variable with mean zero and standard deviation σ L. The functional form of the labour aggregate takes the form L t = [ ] ξ H L 1+ω H,t + ξ N L 1+ω N,t + ξ X L 1+ω 1 1+ω X,t (3) making employment in the different sectors of the economy imperfect substitutes: ω controls the degree of substitutability between employment in different sectors. 7 In Equation (3), L H,t stands for hours worked in the home-tradable goods producing sector, L N,t stands for hours worked in the non-tradable goods producing sector and L X,t stands for hours worked in the commodity-exporting goods producing sector. The parameters ξ H, ξ N and ξ X govern the relative desirability of supplying labour to each sector. Households enter the period with K j,t units of capital from sector j {H, N, X}, B t units of risk free bonds denominated in domestic currency and Bt units of risk free bonds denominated in foreign currency. During the period, the household supplies labour and capital to the domestic production sector, receives profits, Γ j,t, from these sectors, and pays a lump sum tax, T t, to the government. The household uses its income to purchase new domestic and foreign bonds, to invest in new capital in sector j {H, N, X}, I j,t, and to purchase consumption goods. The resulting flow budget constraint is given by: P t C t + P I,t I j,t + B t+1 + S t Bt+1 R t 1 B t j {H,N,X} +R F t 1S t B t + j {H,N,X} (W j,t L j,t + R j tk j,t + Γ j,t ) T t 7 When ω = labour is perfectly substitutable between sectors. 5

6 where P t is the consumer price index, P I,t is the price of the aggregate investment good and W j,t and R j t are the wage rate and rate of return on capital in sector j. R t and Rt F are the rates of return on risk-free bonds in domestic and foreign currency. S t is the nominal exchange rate, the domestic price of foreign currency. The stock of capital in sector j evolves according to: K j,t+1 = (1 δ) K j,t + Ṽt [ 1 Υ ( Ij,t I j,t 1 )] I j,t (4) where δ is the capital depreciation rate and Υ is an investment adjustment cost with the standard restrictions that in steady state Υ( ) = Υ ( ) = and Υ ( ) >. V t is a process that governs the efficiency with which investment adds to the capital stock which we assume to follow, ( ) t 1 Ṽ t = v V t (5) z I where z I is the differential growth rate of real investment over the growth rate of labouraugmenting technology, z, and Ṽt is a stationary autoregressive process that affects the marginal efficiency of investment of the form: ln V t = ρ V ln V t 1 + u V,t (6) where ρ V < 1 and u V,t is an iid random variable with mean zero and standard deviation σ V. On the balanced growth path I j,t can be shown to grow at z z I. The term in the left hand side of Equation (4), Ṽ t I j,t, grows at z. Thus, the trend in Ṽt is necessary for balanced growth if real investment grows faster than real consumption, as is the case here. As the real rental rate on capital is stationary, the household s budget constraint implies that the growth rate of real consumption, z, must equal the growth rate of the capital stocks. The trend in Ṽt offsets the differential growth that real investment brings to the capital accumulation equations. As explained by Schmitt-Grohe and Uribe [23], to ensure stationarity we link the foreign interest rate to the net-foreign asset position. In particular, the interest rate on foreign bonds is given by [ ( ) ] Rt F = Rt St Bt exp ψ b b + NGDP ψ b,t (7) t where R t is the foreign interest rate, b is the steady-state net foreign asset-to-gdp ratio and NGDP t is nominal GDP. ψ b,t is a risk-premium shock that follows the process: ψ b,t = ρ ψ ψb,t + u ψ,t (8) where ρ ψ deviation σ ψ. < 1 and u ψ,t is an iid random variable with mean zero and standard 6

7 2.2 Final goods producing firms Final consumption goods Final consumption goods are produced by a representative competitive firm with the technology: [ ] η C t = γ 1 η η + γ 1 η 1 η η η 1 T,t C T,t η 1 N,t C N,t where C N,t is the output of the non-traded sector that is directed towards consumption and has price P N,t while C T,t is the output of the traded sector that is directed towards consumption and has price P T,t. The deterministic processes γ T,t and γ N,t ensure, as in Rabanal [29], that expenditure shares remain stationary along the balanced growth path. 8 C T,t is itself a composite of domestically- and foreign-produced tradable goods produced according to the following technology C T,t = (C H,t) γ H (C F,t ) γ F (γ H ) γ H (γf ) γ F The Cobb-Douglas specification guarantees that the expenditure shares in the tradable consumption basket remain constant. This assumption is convenient to find the normalisations to make the system stationary. Otherwise, γ H and γ F would have to trend to keep nominal expenditure shares constant in steady state. The trends in γ H and γ F together with the differential growth rate of the home-tradable producing goods, z H, and the differential growth rate of the foreign goods producing sector, z, would determine the differential growth rate of the tradable basket, that is, z T. But to find the trends in γ H and γ F one must know z T. The non-traded, home-produced traded and imported consumption goods are all bundles of a continuum of imperfectly substitutable goods: 9 ( 1 C j,t θ j ) 1 θ θ 1 θ C j,t (i) j di The zero-profit condition implies that the price index of the final consumption good is given by P t = [ ] γ T,t P 1 η T,t + γ N,t P 1 η 1 1 η N,t (9) and the price index of the tradable consumption good, in turn, is given by: Final Investment Goods P T,t = (P H,t ) γ H (P F,t ) γ F (1) Final investment goods are produced by a representative competitive firm with the technology: I t = zv t (I T,t ) γi T (IN,t ) γi N (γt I T (γ I )γi N )γi N 8 See the online appendix for details about the normalisations. 9 This is also the case for investment, I j,t for j {H, N, F }. 7

8 where I N,t is the output of the non-traded sector directed towards the production of investment, I T,t is the output of the traded sector that is directed towards investment and z v is a productivity trend that jointly with the growth rates of I T,t and I N,t determines the steady state growth rate of final investment, that is z I. 1 I T,t is, as before, a composite of domestically-and foreign produced tradable goods that is produced according to the technology The corresponding price indices are and I T,t = (I H,t) γi H (IF,t ) γi F (γ I H )γi H (γ I F )γi F P I t = (P I T,t) γi T (P N,t ) γi N (11) P I T,t = (P H,t ) γi H (PF,t ) γi F (12) As the shares of non-tradable, domestically-produced tradable and imported goods in the investment and consumption composites differ, the price of final consumption goods, P t, will, in general, differ from the price of investment goods, P I,t, as will the price of tradable consumption goods, P T,t, differ from the price of tradable investment goods, P I T,t. 2.3 Intermediate goods producing firms There are four intermediate good producers: commodity firms, non-tradable firms, domestic tradable firms and importing firms. We describe each in turn Commodity-exporting firms Commodity firms produce an homogeneous good in a perfectly competitive market using the Cobb-Douglas production function: Y X,t = A t ZX,t (K X,t ) α X (Z t L X,t ) 1 α X (13) where Z t is a labour-augmenting technology shock, common to all producing sectors, whose growth rate, z t = Z t /Z t 1, follows the process below ln z t = (1 ρ z ) ln z + ρ z ln z t 1 + u z,t (14) and z > 1 determines the trend growth rate of real GDP, Y t. ρ z < 1 and u z,t is an iid random variable with mean zero and standard deviation σ z. The sector-specific productivity process, Z X,t, follows Z X,t = z t XZ X,t (15) 1 Ireland and Schuh [28] and Justiniano et al. [211] are examples of closed economy models with a trend in the price of investment goods and a wedge between the growth rates of real investment and real output. 8

9 where z X > determines the differential growth rate, along the balanced growth path, between Y X,t and Y t, that is between output in the commodity-exporting sector and real GDP. The stationary process Z X,t gives rise to temporary departures from the differential trend by ln Z X,t = ρ X ln Z X,t 1 + u X,t (16) In Equation (13) A t is a stationary technology shock, also common to all sectors, that follows the process ln A t = ρ a ln A t 1 + u A,t (17) where ρ A < 1 and u A,t is an iid random variable with mean zero and standard deviation σ A. Commodity producers take prices as given. These prices are set in foreign currency terms in world markets and are unaffected by domestic economic developments. Specifically, we assume that the price of commodities, in foreign currency terms, is equal to P X,t = κ t P t (18) where Pt is the foreign price level and κ t, which governs the relative price of commodities, follows the exogenous process: ( ) z t κ t = exp (κ t ) (19) zx where z is the differential growth rate of foreign output and zx is the differential growth rate of foreign production of commodities. The drift in the relative price of commodities reflects the relative productivity growth of the commodity sector and the foreign economy. 11 Transitory shocks to commodity prices follow κ t = (1 ρ κ )κ + ρ κ κ t 1 + u κ,t (2) where ρ κ < 1 and u κ,t is an iid shock with zero mean and standard deviation σ κ. For the stochastically detrended variables, κ determines the unconditional mean of the terms of trade and, in turn, is one of the determinants of the economy s steady state. In estimation, we allow for breaks in κ and in σ κ, possibly occurring at different dates in the sample. The law of one price holds for commodities, which means that their price in domestic currency terms is P X,t = S t P X,t (21) Non-tradeable goods producing firms Non-tradeable firms sell differentiated products, which they produce using the Cobb- Douglas production function: Y N,t (i) = A t ZN,t (K N,t (i)) α N (Z t L N,t (i)) 1 α N (22) 11 The productivity trend in the foreign production of commodities must equal the productivity trend in the domestic production of commodities for balanced growth, that is z X = z X. 9

10 Z N,t is sector-specific productivity process that follows Z N,t = z t NZ N,t where z N > and Z N,t are transitory deviations from the sector-specific trend that follows ln Z N,t = ρ N ln Z N,t 1 + u N,t (23) where ρ N < 1 and u N,t is an iid random variable with mean zero and standard deviation σ N. Firms can only change prices at some cost, following a Rotemberg [1982] pricing mechanism: 12 ( ) 2 ψ N PN,t (i) 2 Π N P N,t 1 (i) 1 P N,tY N,t where ψ N governs the size of the price adjustment cost and Π N is the steady state inflation rate of non-tradable goods prices. Aggregate non-tradable output is defined by the Dixit-Stiglitz aggregator: ( 1 Y N,t Y N,t (i) θ N 1 θ N di ) θ N θ N Domestic tradeable goods producing firms Domestic tradable firms produce differentiated products using the Cobb-Douglas production function Y H,t (i) = A t ZH,t (K H,t (i)) α H (Z t L H,t (i)) 1 α H (24) Z H,t is a stationary sector-specific TFP shock that follows Z H,t = z t HZ H,t where z H > and Z H,t are temporary deviations from that trend, ln Z H,t = ρ H ln Z H,t 1 + u H,t (25) where ρ H < 1 and u H,t is an iid random variable with mean zero and standard deviation σ H. Like their non-tradable counterparts, tradable firms can only change prices at some cost, following a Rotemberg [1982] pricing mechanism: ( ) 2 ψ H PH,t (i) 2 Π H P H,t 1 (i) 1 P H,tY H,t where ψ H governs the size of the price adjustment cost and Π H is the steady state inflation rate of domestic-tradable goods prices. Domestic tradable output, Y H,t is an aggregate of the output of each of the domestic tradable firms, ( 1 Y H,t Y H,t (i) θ H 1 θ H di ) θ H θ H 1 12 We assume that these price adjustment costs do not affect the cash flow of firms, but only affect their objective function (see De Paoli et al. [21] for a discussion of this approach). Therefore, they do not appear in the resource constraint or net export equations. Assuming instead that these adjustment costs are real costs would yield equivalent results as quadratic terms do not appear in the linearized system. 1

11 2.3.4 Importing Firms Importing firms purchase foreign good varieties at the price ςs t Pt and sell them in the domestic market at price P F,t (i). The parameter ς represents a subsidy to imported firms, funded by lump-sum taxation. We set the subsidy equal to ς = (θ F 1)/θ F, thereby ensuring that markups in this sector are zero in equilibrium. Importing firms can only change prices at some cost, following a Rotemberg [1982] pricing mechansim ψ F 2 ( PF,t (i) Π F P F,t 1 (i) 1 ) 2 P F,t Y F,t 2.4 Foreign sector, net exports and the current account Following Gertler et al. [27], we postulate a foreign demand function for domestically produced tradable goods, CH,t, of the form C H,t = γ H,t ( ) η PH,t S t P t Foreign output, Ỹ t, follows the non-stationary process Ỹ t = Z t (z ) t Y t Ỹ t (26) where z > captures the differential steady state growth rate between real GDP in the domestic and the rest of the world. Transitory deviations from foreign trend growth are captured by Yt which follow ln Y t = ρ Y ln Y t + u Y,t (27) where ρ Y < 1 and u Y,t is an iid random variable with mean zero and standard deviation σy. Foreign inflation is assumed to follow and the foreign interest rate follows ln Π t = (1 ρ Π) ln Π + ρ Π ln Π t 1 + u Π,t (28) ln R t = (1 ρ R) ln R + ρ R ln R t 1 + u R,t (29) where ρ Π < 1 and ρ R < 1 and the iid shocks u Π,t and u R,t standard deviations σπ and σ R. Net exports are given by: have zero mean and NX t = P H,t C H,t + P X,t Y X,t P F,t (C F,t + I F,t ) (3) and so the current account equation is given by: S t B t+1 = R F t 1S t B t + NX t (31) 11

12 2.5 Monetary Policy The domestic central bank follows a Taylor rule that responds to deviations of output growth and inflation from their steady-state levels ( ) ( ) [ ( ) ( )] Rt Rt 1 Πt Yt ln = ρ r ln + (1 ρ R ) φ π ln + φ y ln + u R,t (32) R R Π zy t 1 where Π t = P t /P t 1 is the inflation rate in terms of final consumption goods prices and Π is the central bank s inflation target. 2.6 Market Clearing Market clearing for investment goods requires that production of these goods equals to quantity demanded by the three domestic production sectors I t = I h,t + I n,t + I x,t (33) For the non-tradable, domestic tradable and import sectors, market clearing requires that the quantity produced equals the quantity demanded: Nominal GDP is defined as: and real GDP is defined as: 2.7 Balanced Growth Y N,t = C N,t + I N,t (34) Y H,t = C H,t + C H,t + I H,t (35) Y F,t = C F,t + I F,t (36) NGDP t = P N,t Y N,t + P H,t Y H,t + P X,t Y X,t (37) Y t = P N P Y N,t + P H P Y H,t + P X P Y X,t (38) A novel feature of this model as that of Rabanal [29] is the existence of trends in aggregate as well as sector-specific productivity. Next, we describe how the variables behave along a balanced growth path and the normalisations that induce stationarity. Along a balanced growth path aggregate variables, including GDP, consumption and the capital stock, grow at the rate of aggregate productivity, z. Sectoral variables, such as output of non-tradable goods, Y N,t, and the quantity of these goods that enter consumption and investment baskets, that is, C N,t and I N,t, grow at aggregate productivity adjusted by the sector specific trend. For example, in steady state the growth rate of non-tradable output is (1 + z)(1 + z N ). Balanced growth requires the shares of each sector in nominal GDP to be constant. For this to hold, the relative prices of each sector must trend by the reciprocal of the 12

13 sector-specific productivity growth rate. So, for example, the relative price of nontradable goods to the price of consumption goods, that is, P N,t /P t, must grow at (1+z N ) 1 along a balanced growth path. When bundles are Cobb-Douglas expenditure shares are constant and balanced growth is satisfied regardless of trends in relative prices because income and substitution effects are offsetting. However, in the more general CES specification for the bundles, balanced growth will be achieved provided that the weights satisfy γ the following processes: γ N,t = N γ (1+z N and γ ) η 1 T,t = T (1+z T. ) η 1 3 Empirical Strategy The structural parameters can be thought of in two categories: those that can only determine dynamics persistence parameters, adjustment cost parameters, policy rule parameters and standard deviations and parameters that, in addition to influencing the dynamics, pin down the steady state. Like Adolfson et al. [27], we calibrate most parameters that determine the steady state. The habits parameter, h, and the long-run level of commodity prices in the final steady state, 1 + κ, however, are estimated. We estimate the remaining parameters. 3.1 Calibration We calibrate for two reasons. First, not all parameters are well identified given the usual choice of observable variables. Second, estimation could imply a steady state at odds with the sample means in the data. We set these parameters so that the balanced growth path is in line with the first moments of the data. The traditional approach of matching sample means seems inappropriate in our case because we postulate a possible break in the long-run level of the terms of trade, which in turn leads to changes in unconditional means. We therefore focus on matching the features of the data over the first part of the sample, before commodity prices started to rise rapidly in the early 2s. To be precise, we calibrate the model s parameters to match means over the period 1993 to 22, which is a period of stability in the terms of trade. In the initial steady state, we first set κ to 1. Before other parameters are calibrated, this choice is a normalisation. After that, of course, a change in κ changes the steady state. For the data to be consistent with the model in estimation, the index of real commodity prices must be re-normalised to average 1 over the sub-sample. Our calibration strategy is as follows. We calibrate the model at a quarterly frequency. We assume that the steady-state rate of labour augmenting TFP growth, z, is 1.49, which matches the average growth rate of per capita GDP over our sample. 13 We set the central bank s target inflation rate, Π, equal to This delivers an average annual inflation rate of around 2.5 per cent, which is the middle of the central bank s stated 13 We calibrate this parameter using the average growth over our full sample of data rather than the shorter 1993 to 22 sample because the shorter sample featured an unusually rapid period of economic growth in Australia associated with a steep recovery from a deep recession in the early 199s and a period of rapid productivity growth due, in part, to a series of microeconomic reforms in the 198s. Consequently, the full-sample average is likely to better reflect the average long-run TFP growth rate. 13

14 inflation target. We set the household s discount rate, β, equal to Together, these three parameters match the steady state nominal interest rate to the sample of the Cash Rate of 6(?) per cent. We set the sector-specific productivity growth differentials, z N and z H so that the inflation rates of tradable and non-tradable goods match their rates in the data. So, we set z N = to ensure that, on average, non-tradable prices rise faster than the CPI. And we set z H to Given this value and the foreign productivity growth differential, z = 1.33, set to match the average growth rate of Australia s major trading partners at PPP, the steady state of tradables goods inflation in the model matches that in the data. We set the capital shares in each sector, α N, α H and α X to.358,.438 and.7, reflecting their average values in national accounts data. 14 The markup parameters, θ N, θ H and θ F are set so that each sector has an an average markup of 1 per cent. The price adjustment costs parameters that determine the slope of Phillips curves, however, are estimated. We set the parameter governing the elasticity of labour supply, η, we set to 2, which is a standard value in the literature. The parameter governing the willingness of workers to move between sectors, we set to 1, in line with Horvath [2]. We set the parameters ξ N, ξ H and ξ X to 1, 29 and This ensures that the share of hours worked in each sector in the model broadly matches that in the data. The shares in the Cobb-Douglas bundles are set to match averages in the data. Thus we set, γ F to.357, γ H to 1 γ F, γn I to.664, γi T to 1 γi N, γi F to.828 and γi H to 1 γi F. The parameters, γh, γ N and γ T, are set to approximate the share of exports in GDP and the share of non-tradable and tradable goods in the domestic consumption basket in the data. We set γh to.877 and γ N and γ T to.48 and.52. Table 2 compares the moments implied by the model s steady state to their empirical counterparts. At the calibrated parameters values of Table 1 the model s steady state does quite well. Investment growth in the model s steady state is somewhat lower than in our sample. Because investment is quite volatile and can fall significantly in recessions, it is likely that the growth rate of investment in our sample (which does not have a recession) is overstated. If we extend the sample to begin in 199:Q1 which includes a recession the average growth rate of investment is We set z v so as to match the rate of inflation of investment goods prices, which in turn, implies a growth rate of investment of 3.43 per cent. 3.2 Estimation We use Bayesian methods, as is common in the estimated DSGE literature. 15 Our case, however, is non standard because we allow for structural change and jointly estimate two sets of distinct parameters: the structural parameters of the model, ϑ, that have continuous support and the dates of structural changes, T = (T κ, T σκ ) that have discrete support; T κ is the date break in the mean and T σκ is the date break in the variance of 14 The data appendix provides additional detail regarding our classification of industries into tradable, non-tradable and commodity-exporting. 15 See An and Schorfheide [27] for a description of these techniques. 14

15 Table 1: Calibrated Parameters Parameter Description Value β Household discount factor δ Capital depreciation rate.5 ν Labour supply parameter 2 ω Intersectoral labour supply elasticity 1 ξ N Constant on non-tradable labor supply 1 ξ H Constant on tradable labour supply 29 ξ X Constant on commodities labour supply 4167 ψ b Risk premium.1 γ N Non-tradables consumption weight.48 γ H Home-produced tradables weight.643 γn I Non-tradables investment weight.664 γh I Home-produced tradables investment weight.172 γh Determinant of foreign demand.877 η Elasticity of substitution.8 η Elasticity of substitution.8 z Steady-state TFP growth 1.49 z v Investment growth rate differential 1.35 z N Non-tradable growth differential.999 z H Home tradable growth differential 1.2 z X Commodity growth differential 1. z Foreign growth differential 1.33 α N Capital share in non-tradables.358 α H Capital share in tradables.438 α X Capital share in commodities.7 Π Domestic inflation target 1.62 Π Foreign inflation target 1.55 θ N Markup in non-tradables 11 θ H Markup in home tradables 11 θ F Markup in imports 11 b Steady state net foreign assets Notes: 15

16 Table 2: Steady State Properties of the Model Average Target Model Macro Aggregates (annual per cent) Per capita output growth Per capita investment growth Inflation Tradable inflation Non-tradable inflation Investment deflator inflation Expenditure (per cent of GDP) Consumption Investment Exports Consumption basket ( per cent of consumption) Non-tradable consumption Home tradable consumption Imported tradable consumption Investment basket (per cent of investment) Non-tradable investment Home tradable investment Imported investment Exports (per cent of exports) Resource exports Other exports Employment (per cent of hours worked) Non-tradable Home tradable Mining Notes: Model ratios calculated at initial regime with κ = 1. and h =.5. 16

17 commodity prices. We set the trimming parameter for both date breaks to 25 per cent of the sample. This implies, in our case, the minimum length of a segment to be 2 observations. Next, we describe how we construct the joint posterior density of ϑ and T: p(ϑ, T Y) L(Y ϑ, T)p(ϑ, T), (39) where Y {yt obs } T t=1 is the data and yt obs is a n obs 1 vector of observable variables. The likelihood is given by L(Y ϑ, T), the priors for the structural parameters and the date breaks are taken to be independent, so that p(ϑ, T) = p(ϑ)p(t). We use a flat prior for T so p(t) 1, which is proper given its discrete support. Kulish and Pagan [212] discuss how to construct L(Y ϑ, T) in models with forward-looking expectations and structural changes. Appendix C describes the posterior sampler. We estimate the model using quarterly Australian macroeconomic data for the period 1993Q1 to 213Q4. The starting date coincides with the start of inflation targeting in Australia and represents a period over which the macroeconomic policy environment has been broadly stable. Our data series includes aggregate and sectoral variables and foreign variables. The aggregate data include real GDP, investment, consumption, net exports, hours worked, the cash rate, trimmed mean inflation and the percentage change in the nominal exchange rate. The national accounts variables and hours are all expressed in per capita terms and seasonally adjusted. Output, investment, consumption and hours all enter in percentage changes, while net exports enters as a share of nominal GDP. We also include two sectoral variables in the model: the inflation rate of non-tradable goods and the ratio of nominal non-tradable consumption to aggregate nominal consumption. The foreign variables that we include in the model are output growth, interest rates and inflation. We take the growth rate of the Australian major trading partner GDP series constructed by the Reserve Bank of Australia as the measure of foreign output growth. For interest rates we use the average of the policy rates in the US, the Euro area and Japan. 16 For the foreign inflation rate, we use the trade-weighted average inflation rate of Australia s major trading partners. The 14 series we use in estimation are shown in Figure 2. Appendix A contains a complete description of the data sources, calculations and transformations. We add measurement error in estimation as is standard in the literature. We calibrate the variance of the measurement errors to 5 per cent of the variance of each observable series. Macroeconomic data are measured with noise and the economic concepts in the model do not always match the measures in the data. Take real output for example. Real output is constructed using chain volume measures which are subject to revision whenever the reference period is changed. The model measure of real output, however, is constructed at steady state relative prices so the reference period does not change. Steady state relative prices change when the long-run level of the terms of trade changes, and our measurement equations change as well, this is not equivalent to chain-volume linking. 16 Prior to the introduction of the euro, we construct this series using the German policy rate. 17

18 Figure 2: Observable variables.4 Output growth.1 Investment growth.2 Consumption growth Net exports to GDP.45 Non tradable consumption to consumption.2 Nominal interest rate Nominal exchange rate x 1 3 Inflation Non tradable Inflation Commodity Prices.2 Hours worked.2 Foreign output growth x 1 3 Foreign inflation.15 Foreign nominal interest rate Priors For the parameter of most interest to us, the long-run level of commodity prices in the final regime, we choose a uniform prior over the domain.25 to 3.5 over the change in κ, that is, we put a flat prior over κ. Notice that, we allow the steady-state of relative commodity price to have declined by 25 per cent, increased by 35 per cent or taken any value in between. We choose the same prior for σ f κ and σ i κ, the standard deviations of shocks to commodity prices in the two regimes. We choose loose beta distributions on the autoregressive parameters and inverse gamma distributions on the standard deviations of the shocks. 17 For the parameters of the monetary policy rule we set a prior mean of 1.5 for the response of the Cash Rate to inflation and of.3 for the response to real output growth. These choice are in line with the literature. Table 4 summarises the priors. 17 These choices are standard in the literature. See An and Schorfheide [27]. 18

19 4 Results 4.1 Date breaks Figure 3 shows the cumulative posterior density of T κ, the date break in the unconditional mean, and cumulative posterior density of T σκ, the date break of the variance, that is the date break for 1 + κ and the date break for σ κ. The data strongly prefer 23:Q2 for the date break in the unconditional mean. The probability that the break occurred in this quarter is around 95 per cent and there is some probability that it occurred in the next few quarters. Our estimate of T κ is close to that of Gruen [211] who dates the start of boom to 22:Q2. Single equation Bai and Perron [1998] tests place the date break in κ a quarter later, that is 23:Q3. The date break in volatility, T σκ, shown in the bottom panel shows, is estimated to have occurred after the increase in the unconditional mean. The posterior density for T σκ is bi-modal. It peaks in 25:Q2 and then again in the second quarter of 28:Q2. Figure 3: Posterior cumulative distributions of date breaks 1 Date break in the mean.8 Cumulative probability q2 2q4 23q2 25q4 28q2 1 Date break in the variance.8 Cumulative probability q2 2q4 23q2 25q4 28q2 4.2 Structural parameters In estimation we allow for breaks in κ and σ κ because we want to give the model a chance to fit the data without necessarily having to resort to a change in κ. As it turns out, the data strongly prefer the specification in which both κ and σ κ increase. The estimation 19

20 Figure 4: Posterior distribution of κ κ could have well chosen to explain the fluctuations in commodity prices post-23 with an increase in volatility and no increase in the unconditional mean. Figure 4 shows the posterior distribution of κ. The density is bounded away from zero and the long-run level of commodity prices 1 + κ is estimated to have increased by around 4 per cent, with a distribution that ranges between 3 and 5 per cent. The posterior distribution significantly shrinks the uncertainty relative to the range of our uninformative prior on κ which ranges from -25 per cent to 35 per cent. Using the tests of Bai and Perron [1998] on the commodity price series points to a 9 per cent increase of the long-run level of commodity prices. But in forward-looking general equilibrium, a 9 per cent increase of the long-run level of commodity prices has implications which are not in the data of other observed domestic endogenous variables. Our estimate is 4 per cent and the single equation one is 9 per cent. Clearly, the other observables serve to moderate the estimated increase in the long-run mean. One may, therefore wonder, if our estimate of κ, would be any different from zero if we were to estimate our model after having removed real commodity prices from the set of observable variables. In fact, we have run this estimation and still find statistically significant evidence of a 2 per cent increase in κ. At a more general level this is an important result: cross-equations restrictions permits us to make inferences about structural breaks in unobservable series. Figure 5 shows the posterior distribution for the ratio of the standard deviations of shocks to commodity prices in the two regimes, that is σ κ/σ κ, where we use the notation that σ κ corresponds to the post-break one. The distribution has no mass at unity or values below. There is no likelihood that the standard deviation of commodity price 2

21 Figure 5: Posterior distribution of σ f κ/σ i κ σ f κ / σi κ shocks has fallen or stayed the same. In fact, the data point to the volatility of shocks to commodity prices having more than doubled. Below we study some of the macroeconomic implications of these changes, but before we briefly discuss estimates of other parameters. Table 3 also summarises the estimates of other parameters. The monetary policy rule parameters reveal that there is persistence in the setting of the policy rate and that the policy rate responds relatively more strongly to inflation than it does to output growth. Habits and investment adjust costs are important; the data prefer some additional persistence, relative to the priors, stemming from these parameters. We also find heterogeneity in the degree of price stickiness across sectors. At the mode the slope of the Phillips curve in the tradable sector is 5 times steeper than in the non-tradable sector which is in turn steeper than in the importing goods producing sector. The parameters of the exogenous process are reported in Table Estimated transitional dynamics To get a sense of the magnitudes involved we compute the transitional dynamics implied by the posterior distribution of κ for real commodity prices and for the price of nontradable goods. We sample from the joint posterior distribution of date breaks and structural parameters. Then at each sampled value, we compute the path of the nonstochastic steady state: this is the path the economy would have taken in the absence of shocks but in the presence of κ occurring at some T κ. Notice that according to Equation (2) a change in κ induces a slow transition towards the new long-run value because the process is persistent. In fact the contemporaneous impact is attenuated by the persistence of the process, is given by (1 ρ κ ) κ. Figure 6 shows the observed real 21

22 Table 3: Prior and Posterior Distribution of Structural Parameters Prior Distribution Posterior Distribution Variable Shape Mean Std Dev. Mode Mean 5 % 95 % Commodity Prices κ Uniform [-.25,3.] σ κ Inv. Gamma σ κ Inv. Gamma ρ κ Beta Monetary Policy Rule ρ R Beta φ π Normal φ y Normal Frictions h Beta Υ Normal Slope N Gamma Slope H Gamma Slope F Gamma Notes: Slope N = 1(θ N 1)/ψ N, Slope H = 1(θ H 1)/ψ H, Slope F = 1(θ F 1)/ψ F 22

23 Table 4: Prior and Posterior Distribution of Shock Processes Prior Distribution Posterior Distribution Variable Shape Mean Std Dev. Mode Mean 5 % 95 % ρ H Beta ρ N Beta ρ X Beta ρ ζ Beta ρ v Beta ρ L Beta ρ z Beta ρ A Beta ρ ψ Beta ρ y Beta ρ r Beta ρ π Beta σ H Inv. Gamma σ N Inv. Gamma σ X Inv. Gamma σ ζ Inv. Gamma σ v Inv. Gamma σ L Inv. Gamma σ z Inv. Gamma σ A Inv. Gamma σ r Inv. Gamma σ ψ Inv. Gamma σ y Inv. Gamma σ r Inv. Gamma σ π Inv. Gamma Notes: 23

24 Figure 6: Observed and long-run commodity prices Observed real commodity prices Long run real commodity prices commodity price series we use in estimation (in levels) and the distribution of the nonstochastic path of real commodity prices implied by our posterior estimates. Most date breaks happen in 23:Q2 and from that time, the grey paths are anticipated (because the process is persistence) even when the shock to κ in 23:Q2 is not. After the break, the forecasts for commodity prices in each quarter, for the most part, implies significant falls in commodity prices. This is consistent with the Reserve Bank of Australia s terms of trade forecast since The difference between observed commodity prices and the implied fundamental level, so to speak, is the result of an increase in the volatility of shocks to commodity prices. What we find remarkable is that we have not insisted that the long-run level had to change, all the variation could have been picked up by volatility, but all observables (including commodity prices) point to an increase in the unconditional mean. It is interesting to look at similar implication for the price of non-tradable goods. Although our model does not have housing sector, an important determinant of nontradable inflation in the data comes from the housing sector. 19 Figure 7 shows the observed relative price of non-tradables goods and the posterior distribution implied by the transition induced by κ. Recall that because there is wedge between non-tradable inflation and inflation, this relative price trends and the rate at which it trends is the same for both balanced growth paths. According to Figure 7, the relative price of nontradables goods is well explained by the shift in the long-run level of the terms of trade. 18 See Figure 4 in Plumb et al. [213]. 19 Future research could extend the model to include a housing sector and study the implication for housing prices. 24

25 Figure 7: Observed and long-run non-tradable prices Long run P N / P Observed P N / P Variance Decompositions The estimated changes in the unconditional mean and volatility bring about changes in the contributions of the various shocks. The change in κ changes the steady state, in particular, it changes the relative size of the sectors. For instance, the commodity sector s share of exports increases from 35 to 52 per cent. This change alone alters the relative contribution of shocks to the business cycle, even if the standard deviation of the shocks does not change. But in our case, shocks to commodity prices become more important. To measure the implications of these changes we compare variance decomposition at the mode for some variables of interest in two regimes: a low regime, κ = 1 and σ κ =.5) and a high regime, κ = 1.42 and σ κ = Shocks to commodity prices and shocks to the productivity of the commodity-exporting sector explain little of the fluctuations in inflation. However, shocks to the productivity of the commodity-exporting sector explain 27 per cent of the variance of output growth in the low regime and around half of the variance post 27. Shocks to real commodity prices explain in the high regime over 5 per cent of the variance of net exports. Many other results are well-known in the literature but we point them out. The nominal exchange rate is mostly driven by risk-premium shocks. However, it is noticeable that the contribution of σ κ increases from half a percent to about 5 per cent. Three quarters of investment growth is explained by shocks to the marginal efficiency of investment. 2 We do not report variance decompositions for the high-κ low-σ κ -regime because the joint posterior implies a low probability for this regime. 25